Curing is one of the most important steps in the tire manufacturing process. During this process, a green tire is formed to the desired shape and the compound is converted to a strong, elastic material to meet tire performance needs. The process of curing, commonly called vulcanization, is usually accomplished under pressure and an elevated temperature provided by the mold. The curing process is energy-consuming and has a strong effect on material properties. To attain an optimal state of cure for different compounds of various dimensions at minimal capital and energy costs requires proper evaluation of the state of cure in a tire. Various numerical models have been proposed to determine the state of cure of rubber compounds in molds. Their applications are limited to simple geometry and boundary conditions. For a tire, which has complex shape and variable boundary conditions, the finite element method appears to be an ideal candidate because of its versatility. In this paper, a commercial finite element code, ABAQUS, is used to determine the temperature history of a tire in the curing press. In order to evaluate the state of cure throughout a tire, a user subroutine, HETVAL, is implemented. In the subroutine, the state of cure is determined based on the temperature history using a selected kinetic model, whose cure rate parameters are obtained from moving die rheometer (MDR) measurements. The heat generation due to chemical reaction is also included. The evaluation of the state of cure using the finite element method is benchmarked using a number of rubber compounds with simple geometries and boundary conditions. Both isothermal and nonisothermal conditions are tested. The predicted temperature history of a tire is then verified by the temperature history obtained from the thermocouples embedded in the tire. Parametric studies are carried out to evaluate the effect of various temperature histories on the state of cure in a tire. The results are used to shorten the curing cycle.
A finite element model was developed to simulate the tire-rim interface. Elastomers were modeled by nonlinear incompressible elements, whereas plies were simulated by cord-rubber composite elements. Gap elements were used to simulate the opening between tire and rim at zero inflation pressure. This opening closed when the inflation pressure was increased gradually. The predicted distribution of contact pressure at the tire-rim interface agreed very well with the available experimental measurements. Several variations of the tire-rim interference fit were analyzed.
Three destructive tire tests, burst pressure, high speed free rotation, and DOT plunger energy are performed to check the ultimate strength of new tires. These tests represent some of the extreme, although unusual, overload conditions that may be applied to a tire. They are used to determine how far above normal service conditions one might take a tire before it reaches its ultimate strength. A nonlinear incompressible rubber model and a nonlinear cord-rubber composite model were used in the tire analyses. Various rubber compounds as well as the rubber in the cord-rubber composite were modeled as nonlinear incompressible Mooney-Rivlin materials. The bimodulus cord and the cord angle change effect due to deformation were also considered. In addition, gap elements were used at the tire-rim interface and between tread grooves where required to provide appropriate boundary conditions. Numerical simulations of these destructive tire tests represent three excellent benchmarks to verify and to evaluate the robustness of a finite element code due to very large strain and deformation occurring in the tire. The numerical results predicted by the finite element tire models agreed very well with the available experimental data.
The finite element analysis of tires under a vertical footprint load requires the use of three-dimensional models. The excessive CPU time required for such models, especially when the tire construction is considered in detail, makes parametric studies difficult and time-consuming. Therefore, one of the principal objectives of finite element program development is to provide an efficient tool for the three-dimensional analysis of tires so that it can be integrated into the design process effectively. In the present study, a systematic finite element procedure is developed for solving loaded tire problems. The principal elements of this procedure are an efficient pre-processor for input generation, a multipoint constraint option to allow the user to exploit any existing symmetry in the problem, and a procedure for generating initial conditions from axisymmetric analyses. This procedure can be used to conduct parametric studies on loaded tires by using a rather coarse mesh and large load steps, thus leading to a significant reduction in CPU time, with a minimum sacrifice in solution accuracy. The efficiency of this procedure is illustrated with the analysis of a radial automobile tire.
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